# LAD: Learning Advantage Distribution for Reasoning

arXiv: https://arxiv.org/abs/2602.20132 · HTML: https://mlsanity.com/paper/2602.20132/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 66 of its 83 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 66)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)

## Built on by (most cited first, 2 of 2)

- [Uniform-Correct Policy Optimization: Breaking RLVR's Indifference to Diversity](https://mlsanity.com/paper/2605.00365/) (2026)
- [Cyclical Entropy Eruption: Entropy Dynamics in Agent Reinforcement Learning](https://mlsanity.com/paper/2605.27954/) (2026)

## Abstract (arXiv)

Current reinforcement learning objectives for large-model reasoning primarily focus on maximizing expected rewards. This paradigm can lead to overfitting to dominant reward signals, while neglecting alternative yet valid reasoning trajectories, thereby limiting diversity and exploration. To address this issue, we introduce Learning Advantage Distributions (LAD), a distribution-matching framework that replaces advantage maximization with learning the advantage-induced distribution. By establishing the equivalence between the optimal policy update and an advantage-based target distribution, we derive a practical LAD objective formulated as minimizing an f-divergence between the policy-induced and advantage-induced distributions. This yields a gradient update that increases likelihood for high-advantage responses while suppressing over-confident probability growth, preventing collapse without requiring auxiliary entropy regularization. LAD incurs no extra training cost compared to GRPO and scales naturally to LLM post-training. In a controlled bandit setting, LAD faithfully recovers the multimodal advantage distribution, validating the theoretical formulation. Experiments on math and code reasoning tasks across several LLM backbones show that LAD reliably improves both accuracy and generative diversity.